Detection of glitches and signal reconstruction using Hölder and wavelet analysis

We present a method based on a local regularity analysis for detecting and removing artefact signatures in noisy interferometric signals. Using Hölder and wavelet transform modulus maxima lines analysis (WTMML) [S. Mallat, W. Hwang, Singularities detection and processing with wavelets, IEEE Transaction on Information Theory 38 (1992) 617–643] in suitably selected regions of the time-scale half-plane, we can estimate the regularity degree of the signal. Glitches that are considered as a discontinuity on the signal show Hölder component lower than a fixed threshold defined for a continuous signal. After detection and signature removal, the signal is then locally reconstructed using Mallat reconstruction formulae. The method has been tested with Herschel SPIRE FTS proto-flight model calibration observations and shows remarkable results. Optimization of the detection parameters has been performed on the correlation coefficient, the scale domain for Hölder exponent estimation and reconstruction for SPIRE FTS signals.